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Given the quadric defined by the equation<br /><br /><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#f«/mi»«mo»=«/mo»«mn»0«/mn»«/math»</span><br /><br />a) The equation defines a {1:SA:=#A}<br /><br />(Choose between <span style="font-style: italic;">ellipsoid</span>, <span style="font-style: italic;">cone</span>, <span style="font-style: italic;">one_sheet_hyperboloid</span>, <span style="font-style: italic;">two_sheets_</span><span style="font-style: italic;">hyperboloid</span>, <span style="font-style: italic;">hyperbolic_</span><span style="font-style: italic;">paraboloid, elliptic_paraboloid, cilinder </span>)<br /><br />b) The condition for defining <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«/math»</span> as an implicit function of <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«/math»</span> in a neighbourhood of a certain point <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mi»x0«/mi»«mo»,«/mo»«mi»y0«/mi»«mo»,«/mo»«mi»z0«/mi»«/mrow»«/mfenced»«/math»</span> is: {1:MC: Any z0 real~z0 must be nonnegative~=z0 must be nonzero~z0 must be positive~z0 can be zero}<br /><br />c) The normal vector to the quadric at the point <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mi»x0«/mi»«mo»,«/mo»«mi»y0«/mi»«mo»,«/mo»«mi»z0«/mi»«/mrow»«/mfenced»«/math»</span> is<br /><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»v«/mi»«mo»=«/mo»«mo»(«/mo»«/math»</span> {1:SA:=#v1}, {1:SA:=#v2}, {1:SA:=-1} <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»)«/mo»«/math»</span><br /><br /><br /><br />
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Thursday, 10 December 2015, 10:53 AM
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